clarkson



(No Model.)

3 SheetsSheet 1. T. CLARKSON. INSTRUMENT PCB DRAWING ARCS 0F CIRCLES.

P atented Mar. 8 1898.

(No Model.) 3 Sheets-Sheet 2.

T. OLARKSON. INSTRUMENT FOR DRAWING ARCS 0F CIRCLES.

Patented Mar. 8, 1898.

(No Model.) 3 Sheets-Sheet "3.

T. CLARKSON. INSTRUMENT FOR DRAWING ARCS 0F CIRCLES. No. 600,357. Patented Mar. 8,1898.

UNITED STATES PATENT OFFICE.

THOMAS CLARKSON, OF SUTTON, ENGLAND.

INSTRUMENT FOR DRAWING ARCS OF CIRCLES.

SPECIFICATION forming part of Letters Patent N 0. 600,357, dated March 8, 1898.

Application fi1ed April 10, 1895. Renewed February 18, 1897. flerial No. 624,076. tNo model.) Patented in England March 14,1S95,No.5,485.

To all whom it may concern:

Be it known that I, THOMAS GLARKSON, a subject of the Queen of England, residing at Sutton, Surrey, England, have invented certain new and useful Improvements in Mathematical Instruments for Use in Drawing Arcs of Circles, (for which I have obtained Letters Patent in Great Britain, No. 5,435, dated March 14, 1895,) of which the following is a specification.

This invention relates to mathematical instruments for use in drawing arcs of circles whose diameters are too great to permit the arcs to be drawn by ordinary compasses. Hitherto a long wire or rod or a trammel has been used as a raidus-arm in drawing such arcs; but these devices are unwieldy and cumbrous and frequently need two operators.

, Moreover, the curved lines produced by such means are more or less wavy or otherwise inaccurate owing to the absence of rigidity from the apparatus. Another common device consists in bendinga thin piece of spring-steel or wood so that it will approximately correspond with three points previously determined upon the required curve, the said spring then constituting a ruler for completing the curve. It is well known, however, that this device does not give a true circular are, for the established reason that a straight spring when bent either by end pressure or by pressure applied to the middle while the ends are supported yields more in the center than toward each end, so that its curve approximates more to a parabola than to a circle.

The object of my invention is to construct a compact and simple instrument wherein a novel form of flexible ruler and means for enabling it to be easily given the desired curvature are combined in such a manner that one operator alone is enabled to draw arcs of great radii with accuracy and facility. The flexible ruler is of resilient material, so formed and so held by bending and retaining devices that it can readily be caused to bend and become an are which will vary in radius with the movement of the adjusting devices, but will always be circular.

According to my invention I construct the flexible ruler of a strip, preferably of metal, with one edge plain and the other shaped otherwise. This strip is widest at the center and tapering off toward the ends. It may be formed as two right-angled triangles with their bases meeting at the center of the plate or joined by a parallel-sided strip and with the apex of each triangle at or toward the end of the plate. This would be approximately correct as a theoretical construction, but as minute differences in temper at different parts of the plate or in thickness or in quality of the metal or material may affect the result I find it desirable to slightly hollow the edge of the plate, so that it becomes not a true triangle. This, however, would depend very much upon circumstances, and the above illustration will serve to indicate the broad principle of the construction.

As an alternative the flexible ruler maybe a thin flat strip, so tapered or reduced from the middle of its length toward its ends that successive parallel measurements of its width taken parallel with the intended axis of ourvature would, if plotted perpendicularly to a straight line, be ordinates of a symmetric hyperbolic segment; or, instead of a plate reduced in width, I may employ a strip or bar whose cross-section is varied in such a manner as to constitute it the equivalent of such a tapered flat strip.

\Vhen the triangulated ruler is employed, I support the ends thereof upon a rigid bar or its equivalent and curve the plate by forcing its center out of a straight line, or, equivalently, I adopt mechanism whereby I am enabled to hold the center still and bend the ends out of a straight line.

Where a strip or templet with one edge parabolic is employed, I curve the templet by applying pressure to its ends, which are specially shaped for a purpose hereinafter stated.

As regards the principles involved in the shaping of the plates it will be sufficient for present purposes to say that they are substantially those well understood in connection with the bending strains ofgirders, it being remembered that in this instance the object is not to prevent the plate from bending, but to cause it to bend always in a true circular are.

It will be readily appreciated that the form or construction of the beam or framework carrying the plate can be greatly varied and that any suitable materials may be employed for that or for the plate, though hitherto I have found that for the plate a high quality of steel gives excellent results.

As a matter of convenience in constructing these instruments I prefer to make the plates of fixed lengths commonly useful, so that they may serve for purposes of measurement and to make the flat edge true, so that it may be used as a straight-edge, and, if desired, to let the plate bear a scale, so that it may be used as a rule, trammel, or for other similar purposes.

In the accompanying drawings, Figures 1 to 7 illustrate constructions of my instrument wherein the triangulated form of flexible ruler is employed. In these drawings, Fig. 1 is a plan, Fig. 2 a front elevation, and Fig. 3 a rear elevation, of one construction of instrument according to my invention. Fig. 4 is a plan, and Fig. 5 a rear elevation,-of another construction; Figs. 6 and 7, a plan and front elevation, respectively.

Like letters indicate like parts throughout the drawings. 1

With reference first to Figs. 1, 2, and 3, A is the resilient triangulated rulerthat is to say, it has one edge A straight and the opposite edge A tapered off toward the ends, as shown. The form of this triangulated ruler is indicated clearly in Fig. 2, in which it is seen in plan quite fiat.

B is a rigid bar provided at each end with jaws B 13*, which engage with the ends of the resilient ruler A. To facilitate this engagement, the ends A of the ruler are squaredv and made wide enough to prevent the ruler from tilting in the jaws, which are sufficiently .Open to put no undue restraint upon the bending of the ruler into arcs.

D is a skeleton arm pivoted at B to lugs on the bar B. Two plungers E pass through the bar B and engage at one end with the flexible ruler A and at their opposite ends with a pair of pins D in the bar. The pins D are screw-threaded to facilitate the setting or preliminary adjustment of the plungers relatively to the ruler A and to the arm G,

hereinafter referred to.

F is a screw-bolt. F is a milled nut thereon engaging with a hemispherical bearing D projecting from the arm D, and F is a knife-edged head engaging with a correspondingly-shaped recess B in the bar B.

The nut F is used to operate the arm D, the free end G of which is used as an index with reference to a graduated scale II, hinged at B to the bar B. By moving the arm D the plungers E are operated to bend the flexible ruler, and simultaneously the index G indicates upon the scale H the curvature of the ruler A corresponding to the position into which the arm D is adjusted. In Figs. 1, 2, and 3 chain-lines indicate the position taken up by the several parts when the ruler A is ample, one with a T-head formed as aknifeedge or rounded. where it engages with the ruler. To reduce for packing the compass of the instrument, the scale H may be folded into the position indicated by dotted lines in Fig. 1.

I prefer to provide stops B in the jaws B B to prevent the plate when dropped into the jaws from passing entirely through them; but one or both ends of the ruler A may, if desired, be permanently secured to or connected with the bar B. The ruler A in all the apparatus herein described automatically unbends itself when the action of the bending or compressing devices is reversed In the alternative construction illustrated in Figs. 4 and 5 I employ a ruler A and bar B as before, but instead of pressing the ruler A from the center I press it from two points A A practically dividing it into three equal lengths. I may press it at more than two points, but two will be sufficient to illustrate my meaning. In this case I may adopt any arrangement of screw and levers for forcing out the plungers E or otherwise curving the plate; but I find a convenient arrangement to be to fix the screw F at the center of the beam and hinge two levers D toward the ends of the beam by hinges at B their free ends coming substantially together, so that one nut F upon the screw may bear upon both the levers, as shown, so as to be able to operate I in this and other arrangements I may dispose the scale and index in any other convenient manner. The ruler A in this instance is substantially the same as in Figs. 1, 2, and 3, the triangular construction before observed being adopted; but as the ruler is moved from two points instead of one the base of each triangle would be approximately at the points A where the power is applied, the piece of the ruler between these two points being of substantially the same width throughout, as at A Fig. 5.

Chain-lines in Fig. 4 show the ruler A bent and the levers and nut in corresponding positions.

As it is desirable to avoid the possibility of undue strain being placed upon the ruler by bending it too much and also to prevent bending or straining the levers, I prefer to provide a stop for this purpose. A convenient way of effecting this is to provide that portion of the lever through which the screwed rod passes with a boss-such, for instance, as

IIO

D Fig. 1-or a collar extension or equivalent so arranged that at the extreme limit allowed in the bending of the ruler A it comes in contact with the bar B and thus stops further movement. The same result would be obtained if this arrangement were reversed and the projection or equivalent provided upon the beam. Other stop devices, however, may be employed in any of the instruments herein described.

The alternative construction illustrated in Figs. 6 and 7 and embodying the triangulated ruler is one in which the two ends A of the ruler A are pivoted by lugs A fixed thereon to arms I, the opposite ends of which are pivoted to a nut I,which latter engages with and can travel upon a screwed rod J, to which is fixed a milled head J. By adjusting the rod J in the nut I the center of the ruler A is thrust in or out by that rod, so that the ruler is bent into a circular arc, its ends being held by the lugs A and arms I, before referred to. To insure the maintenance of the rod J centrally between the two arms 1, those armsare connected by links 1 to a sleeve K, free to slide on the rod.

As an alternative to the indicating mechanism hereinbefore described I may attach a suitable scale to one compressor, so that it will move past an index on the other compressor.

The indicating apparatus in these improved instruments is calibrated by comparison with standard curves and graduated accordingly, preferably to indicate the radii of the arcs as sumed by the templet. The indicating mechanism may be dispensed with if the instrument is to be used for the production of circular arcs and it is not desired to know their radius.

The instruments are made so as to lie flat and steady on a level surface, such as that of a drawing.

To insure the attainment of an accurate templet or ruler, I put it in compression with its straight edge downward, so that its curvature corresponds approximately with a circular arc of convenient radius which has been carefully drawn upon a sheeet of paper. If the plate does not exactly correspond with the drawn arc, those parts of the plate where the curvature is too flat are narrowed by removing part of the metal from the angular or curved edge-for example, until the plate exactly corresponds with the drawn are at all poi nts-excepting only for the short distance at each end, where the small portions of the plate are allowed to remain outside the angular or curved edge to be engaged by the compressors, as before stated; but this may be compensated for by removing a small portion of the metal at the adjacent part of the plate. I have found by trial that a plate made and operated in the manner described will always spring into a circular are whether the bending be much or littlethat is to say, if a plate is made so as to bend exactly to a twelve-inch circle it can be also made to exactly correspond with any circular arc of, say, larger radius by simply allowing its extremities to move apart orits center to approach the chord of the arc.

I claim 1. In a mathematical instrument for use in drawing arcs of circles, the combination with a resilient ruler which is reduced in width from the middle of its length toward each end; of retaining and bending devices arranged to engage the intermediate portion of the ruler and force it outwardly, and separate mechanism arranged to indicate directly the curvature of the ruler, said mechanism having actuating connections with the bending devices; substantially as described.

2. In a mathematical instrument for use in drawing arcs of circles the combination with a resilient ruler A reduced in width from the middle of its length toward each of its ends of a beam B, jaws B at each end of the beam to retain the ends of the, ruler, plungers E, the arm D pivoted to the beam B, screws D, the screw F its nut F and head F and indicating mechanism constituted by the arm G and graduated pivoted scale H substantially as set forth.

3. In a mathematical instrument for use in drawing arcs of circles the combination with a resilient ruler A reduced in width from the middle of its length toward each of its ends, of a beam B, jaws B at each end of the beam to retain the ends of the ruler, plungers E, the arm 1) pivoted to the beam B, screws D and the screw F its nut F and its head F substantially as set forth.

In testimony whereof I have hereto set my hand in the presence of the two subscribing witnesses.

THOMAS CLARKSON.

' WVitnesses:

WM. J NO. TENNANT, HARRY B. GRADY. 

